\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{math_notations}

\usepackage{amsmath}
\usepackage{amssymb}

% For matrixes and vectors
\newcommand{\vect}[1]{{\mathbf{\boldsymbol{{#1}}}}}
\newcommand{\mat}[1]{{\vect{\vect{#1}}}}
\newcommand{\Tr}[1]{{#1}^\top}

% Bold letters 
\newcommand{\bdA}{{\boldsymbol{A}}}
\newcommand{\bdB}{{\boldsymbol{B}}}
\newcommand{\bdC}{{\boldsymbol{C}}}
\newcommand{\bdD}{{\boldsymbol{D}}}
\newcommand{\bdE}{{\boldsymbol{E}}}
\newcommand{\bdF}{{\boldsymbol{F}}}
\newcommand{\bdG}{{\boldsymbol{G}}}
\newcommand{\bdH}{{\boldsymbol{H}}}
\newcommand{\bdI}{{\boldsymbol{I}}}
\newcommand{\bdJ}{{\boldsymbol{J}}}
\newcommand{\bdK}{{\boldsymbol{K}}}
\newcommand{\bdL}{{\boldsymbol{L}}}
\newcommand{\bdM}{{\boldsymbol{M}}}
\newcommand{\bdN}{{\boldsymbol{N}}}
\newcommand{\bdO}{{\boldsymbol{O}}}
\newcommand{\bdP}{{\boldsymbol{P}}}
\newcommand{\bdQ}{{\boldsymbol{Q}}}
\newcommand{\bdR}{{\boldsymbol{R}}}
\newcommand{\bdS}{{\boldsymbol{S}}}
\newcommand{\bdT}{{\boldsymbol{T}}}
\newcommand{\bdU}{{\boldsymbol{U}}}
\newcommand{\bdV}{{\boldsymbol{V}}}
\newcommand{\bdW}{{\boldsymbol{W}}}
\newcommand{\bdX}{{\boldsymbol{X}}}
\newcommand{\bdY}{{\boldsymbol{Y}}}
\newcommand{\bdZ}{{\boldsymbol{Z}}}
\newcommand{\bda}{{\boldsymbol{a}}}
\newcommand{\bdb}{{\boldsymbol{b}}}
\newcommand{\bdc}{{\boldsymbol{c}}}
\newcommand{\bdd}{{\boldsymbol{d}}}
\newcommand{\bde}{{\boldsymbol{e}}}
\newcommand{\bdf}{{\boldsymbol{f}}}
\newcommand{\bdg}{{\boldsymbol{g}}}
\newcommand{\bdh}{{\boldsymbol{h}}}
\newcommand{\bdi}{{\boldsymbol{i}}}
\newcommand{\bdj}{{\boldsymbol{j}}}
\newcommand{\bdk}{{\boldsymbol{k}}}
\newcommand{\bdl}{{\boldsymbol{l}}}
\newcommand{\bdm}{{\boldsymbol{m}}}
\newcommand{\bdn}{{\boldsymbol{n}}}
\newcommand{\bdo}{{\boldsymbol{o}}}
\newcommand{\bdp}{{\boldsymbol{p}}}
\newcommand{\bdq}{{\boldsymbol{q}}}
\newcommand{\bdr}{{\boldsymbol{r}}}
\newcommand{\bds}{{\boldsymbol{s}}}
\newcommand{\bdt}{{\boldsymbol{t}}}
\newcommand{\bdu}{{\boldsymbol{u}}}
\newcommand{\bdv}{{\boldsymbol{v}}}
\newcommand{\bdw}{{\boldsymbol{w}}}
\newcommand{\bdx}{{\boldsymbol{x}}}
\newcommand{\bdy}{{\boldsymbol{y}}}
\newcommand{\bdz}{{\boldsymbol{z}}}

% special caracters
\newcommand{\cA}{{\mathcal A}}
\newcommand{\cB}{{\mathcal B}}
\newcommand{\cC}{{\mathcal C}}
\newcommand{\cD}{{\mathcal D}}
\newcommand{\cE}{{\mathcal E}}
\newcommand{\cF}{{\mathcal F}}
\newcommand{\cG}{{\mathcal G}}
\newcommand{\cH}{{\mathcal H}}
\newcommand{\cI}{{\mathcal I}}
\newcommand{\cJ}{{\mathcal J}}
\newcommand{\cK}{{\mathcal K}}
\newcommand{\cL}{{\mathcal L}}
\newcommand{\cM}{{\mathcal M}}
\newcommand{\cN}{{\mathcal N}}
\newcommand{\cO}{{\mathcal O}}
\newcommand{\cP}{{\mathcal P}}
\newcommand{\cQ}{{\mathcal Q}}
\newcommand{\cR}{{\mathcal R}}
\newcommand{\cS}{{\mathcal S}}
\newcommand{\cT}{{\mathcal T}}
\newcommand{\cU}{{\mathcal U}}
\newcommand{\cV}{{\mathcal V}}
\newcommand{\cW}{{\mathcal W}}
\newcommand{\cX}{{\mathcal X}}
\newcommand{\cY}{{\mathcal Y}}
\newcommand{\cZ}{{\mathcal Z}}
\newcommand{\Cset}{{\mathbb C}}
\newcommand{\Eset}{{\mathbb E}}
\newcommand{\Nset}{{\mathbb N}}
\newcommand{\Pset}{{\mathbb P}}
\newcommand{\Qset}{{\mathbb Q}}
\newcommand{\Rset}{{\mathbb R}}
\newcommand{\Zset}{{\mathbb Z}}
\newcommand{\Diff}{{\mathrm{d}}}

% short commands
\newcommand{\un}[1]{\vect{#1}}
\newcommand{\dpl}[1]{\displaystyle{#1}}
\newcommand{\uw}{\vect{w}}
\newcommand{\uW}{\vect{W}}
\newcommand{\ux}{\vect{x}}
\newcommand{\uX}{\vect{X}}
\newcommand{\uy}{\vect{y}}
\newcommand{\uY}{\vect{Y}}
\newcommand{\uz}{\vect{z}}
\newcommand{\uZ}{\vect{Z}}
\newcommand{\muX}{\vect{\mu}_{\:X}}
\newcommand{\Var}[1]{{\rm Var}\left[ #1 \right]}
\newcommand{\Cov}[1]{{\rm Cov}\left[ #1 \right]}
\newcommand{\Expect}[1]{{\mathbb E}\left[ #1 \right]}
\newcommand{\Econd}[2]{{\mathbb E}_{#1}\left[ #2 \right]}
\newcommand{\Prob}[1]{{\mathbb P}\left( #1 \right)}
\newcommand{\ProbCond}[2]{{\mathbb P}_{#1}\left( #2 \right)}
\newcommand{\pdf}{f_{\un{X}}(\un{x})}
\newcommand{\ech}{\left\{ x_1, \, \dots\,, x_N  \right\}}
\newcommand{\matcov} {\mathbf C}
\newcommand{\matcor} {\mathbf R}
\newcommand{\fcar}[2] {{\mathbf 1}_{#1}(#2)}
\newcommand{\supp}[1] {{\rm supp}\left(#1\right)}
\newcommand{\di}[1] {{\,\mathrm{d}#1}}
\newcommand{\norm}[1] {\left\|#1\right\|}
\newcommand{\tendto}[2]{\xrightarrow[#1\rightarrow#2]{}}
\newcommand{\matr}[1]{\vect{\vect{#1}}}
\newcommand{\idx}{\vect{\alpha}}
\newcommand{\NM}{\Nset^{n_X}}
\newcommand{\Cor}[1]{{\rm Cor}\left[ #1 \right]}

\DeclareMathOperator*{\argmin}{argmin}
\DeclareMathOperator*{\argmax}{argmax}
\DeclareMathOperator*{\diag}{diag}
\DeclareMathOperator{\sgn}{sgn}